basic

Damped Harmonic Oscillator Amplitude Decay Calculator

A(t) = A₀ · e^(−γ·t).

Compute the amplitude of a lightly damped harmonic oscillator (e.g. a pendulum in air, an RLC circuit) at time t. Decay envelope A(t) = A₀ · e^(−γt) where γ = b/(2m) is the damping coefficient. Reports both the amplitude and the energy fraction remaining (which decays as e^(−2γt)).

Marcus Laurent By Marcus Laurent
Published Last reviewed 1 min read

Inputs

m
s⁻¹
s

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

A(t) = A₀·e^(−γt); energy fraction = e^(−2γt).

In depth

Compute the amplitude of a lightly damped harmonic oscillator (e.g. a pendulum in air, an RLC circuit) at time t. Decay envelope A(t) = A₀ · e^(−γt) where γ = b/(2m) is the damping coefficient. Reports both the amplitude and the energy fraction remaining (which decays as e^(−2γt)).